Global Environmental Change 41 (2016) 216–227

Screening robust water infrastructure investments and their trade-offsunder global change: A London example

Ivana Huskovaa, Evgenii S. Matrosovb, Julien J. Haroub,a,*, Joseph R. Kasprzykc,Chris Lambertd

aDepartment of Civil, Environmental and Geomatic Engineering, University College London, London, WC1E 6BT, UKb School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, M13 9PL, UKcDepartment of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO 80309-0428, USAd Thames Water Utility Limited, Clearwater Court, Vastern Road, Reading, RG1 8DB, UK

A R T I C L E I N F O

Article history:Received 6 May 2015Received in revised form 22 October 2016Accepted 28 October 2016Available online 14 November 2016

Keywords:Water resources planningDecision-Making under uncertaintyMany-objective optimizationTrade-off analysisRobust investments

A B S T R A C T

We propose an approach for screening future infrastructure and demand management investments forlarge water supply systems subject to uncertain future conditions. The approach is demonstrated usingthe London water supply system. Promising portfolios of interventions (e.g., new supplies, waterconservation schemes, etc.) that meet London’s estimated water supply demands in 2035 are shown toface significant trade-offs between financial, engineering and environmental measures of performance.Robust portfolios are identified by contrasting the multi-objective results attained for (1) historicallyobserved baseline conditions versus (2) future global change scenarios. An ensemble of global changescenarios is computed using climate change impacted hydrological flows, plausible water demands,environmentally motivated abstraction reductions, and future energy prices. The proposed multi-scenario trade-off analysis screens for robust investments that provide benefits over a wide range offutures, including those with little change. Our results suggest that 60 percent of intervention portfoliosidentified as Pareto optimal under historical conditions would fail under future scenarios consideredrelevant by stakeholders. Those that are able to maintain good performance under historical conditionscan no longer be considered to perform optimally under future scenarios. The individual investmentoptions differ significantly in their ability to cope with varying conditions. Visualizing the individualinfrastructure and demand management interventions implemented in the Pareto optimal portfolios inmulti-dimensional space aids the exploration of how the interventions affect the robustness andperformance of the system.ã 2016 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/).

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1. Introduction

Many urban water systems across the globe face future stressessuch as reduced or shifted water availability due to climate change,increased water demands, more demanding regulatory regimesand heightened service expectations (Ferguson et al., 2013;Hallegatte, 2009; Pahl-Wostl, 2009). Water supply infrastructurein many major cities globally relies on aging assets designed andconstructed over a century ago (Boyko et al., 2012). Refurbishmentof existing infrastructure and capacity expansion is needed to copewith future pressures. Moreover, the uncertainty in future

* Corresponding author.E-mail addresses: iva.huskova83@gmail.com (I. Huskova),

julien.harou@manchester.ac.uk (J.J. Harou).

http://dx.doi.org/10.1016/j.gloenvcha.2016.10.0070959-3780/ã 2016 The Author(s). Published by Elsevier Ltd. This is an open access art

conditions motivates novel approaches that help discover whichcombinations of interventions would work well under a widerange of plausible futures.

Instead of defining “optimality” under historical or narrowlydefined conditions, planners have recently been seeking “robust-ness” for planning under uncertainty (Ben-Haim, 2000; Haasnootet al., 2013; Herman et al., 2015; Lempert et al., 2003). Robustnessas a planning goal is well suited to situations where theprobabilities that govern uncertain future states are uncertainthemselves. Such uncertainties are known as ‘deep’ or Knightianuncertainties (Knight, 1921). For example, assigning probabilitiesto population growth or the effects of climate change on systems isproblematic (Walker et al., 2013). A robust system is one thatperforms well or satisfactorily well over a broad range of plausiblefuture conditions rather than optimally in one. Robustness is

icle under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

I. Huskova et al. / Global Environmental Change 41 (2016) 216–227 217

increasingly incorporated as a goal in many-objective watersystems planning studies (Giuliani et al., 2014; Hamarat et al.,2014; Herman et al., 2014; Kasprzyk et al., 2013, 2012). Planningapproaches seeking robustness have also been investigated in theUK’s water resource planning context (Borgomeo et al., 2014;Korteling et al., 2013; Matrosov et al., 2013a, 2013b) but none ofthose explored the implications of many-objective decision-making and how the trade-offs change when multiple sourcesof uncertainty are considered. Recently, dynamic robustness(Walker et al., 2013) that specifically considers the value offlexibility and adaptation has been explored using the DynamicAdaptive Policy Pathways approach for pre-specified strategies(Haasnoot et al., 2013; Urich and Rauch, 2014) and in multi-objective optimization (Hamarat et al., 2014; Kwakkel et al., 2014).Application of such frameworks by water system planners willrequire them to understand and accept the benefits of embeddingthe search for robustness within automated investment filteringapproaches which historically only considered cost. In our studywe focus on demonstrating how performance trade-offs betweeninvestment packages change when uncertainties are consideredwithin complex real-world water systems. Our goal is tocommunicate to policy makers the increase in understandingand judgement they can obtain by incorporating uncertainty intoautomated intervention evaluation methods.

Urban water supply planners have commonly employednarrowly defined, least-cost decision frameworks to guide capacityexpansions subject to maintaining required service levels (e.g., Hsuet al., 2008; Padula et al., 2013). Planning that does not capture keyconcerns or preferences across major stakeholder groups increasesthe likelihood that policies are viewed as performing poorly(McConnell, 2010) and maladaptative. The optimality assumptionsimplicit to least-cost approaches assume a central planner forwhom expected aggregated costs fully describe their preferencesamongst water supply alternatives. One vision of optimalityinevitably forces a decision maker to prior judgments without theknowledge of the decision’s wider implications (Cohon and Marks,1975). In real planning contexts, an increasingly diverse range ofstakeholder perspectives must be addressed with major publicinvestments and plans (Vogel and Henstra, 2015); this isparticularly the case with decisions involving natural resourcesmanagement (Jackson et al., 2012; Orr et al., 2007; Voinov andBousquet, 2010). The emphasis is no longer only on one vision ofoptimality (e.g. least-cost) but on converging on a plan thataddresses major concerns and acceptably allocates benefitsbetween the major stakeholder groups and economic sectors(Loucks et al., 2005). Generating multiple alternative solutions thatare good with respect to multiple objectives but differ from eachother enables explicit examination of the alternatives and gaininginsight and knowledge about the system (Brill et al., 1982).Methods that clarify the trade-offs across the various benefits andimpacts of portfolios of different supplies and water conservationactions have garnered a more significant role in recent publishedwork (Arena et al., 2010; Beh et al., 2015; Herman et al., 2014;Kasprzyk et al., 2009; Matrosov et al., 2015; Mortazavi et al., 2012;Zeff et al., 2014).

Simple capacity expansion approaches such as least-cost yieldplanning (Padula et al., 2013) are being renewed in many areas ofresource management to incorporate the planning approachesdescribed above. The current UK approach does not consider aportfolio’s robustness, cost, and social and environmental accept-ability explicitly (Dessai and Hulme, 2007). Water planners andregulators recognize the limitations of the current approach andare actively seeking to improve the statutory planning framework(Defra, 2011). Our study aims to reflect the necessity of the currentwater planning policy changes that are being considered. Theseinclude a move from solely least-cost solutions to planning for

resilience and robustness against a wide range of plausible futureconditions whilst considering wider impacts of decisions beyondcost (Environment Agency, 2015). However, the current watersupply system planning framework (Padula et al., 2013) requireswater companies consider intervention yields, i.e., the maximumdaily water supply an intervention can provide, based on historicalflow data. This paper describes a planning approach that explicitlyconsiders both multiple sources of uncertainty and multipleevaluation objectives. We show how considering only historicaldata can lead to poorly performing system designs underhydrological futures considered plausible by national climatemodel results (Centre for Ecology and Hydrology, 2015). In ourproposed system design screening framework the goal ofrobustness and resilience is incorporated explicitly into anautomated intervention selection process. This contrasts withcommon approaches where robustness and resilience are evaluat-ed post-optimization using sensitivity analyses (e.g. ThamesWater, 2014). This provides analysts with a high performing setof robust system designs and the associated trade-offs in benefitsimplied by intervention choices. The benefits of incorporatingmultiple sources of uncertainty into a multi-objective decisionmaking process are demonstrated.

Trade-off analysis has some, but limited, prior history ofinclusion in water resource planning regulations (e.g. CaliforniaDepartment of Water Resources, 2008; UKWIR, 2016). Here weseek a visually communicable approach which enables stakeholderdeliberation about benefits achievable by the water system and itsengineered assets that is compatible with the resilience andparticipatory aspirations of UK water planning (EnvironmentAgency, 2015). Our study demonstrates the importance ofunderstanding how benefit trade-offs change when diversesources of uncertainty are considered. From a policy perspectivethe trade-offs and broader performance requirements help toavoid the myopia of least-cost decision making (Herman et al.,2015). Results aid policy makers to orient their investmentstrategies towards their key requirements and aspirations.

Our study proposes a multi-scenario multi-objective decision-making approach which addresses some limitations of the currentplanning approach. Several conflicting performance goals includ-ing the financial, engineering and environmental performance areconsidered explicitly. Multiple sources of uncertainty in the formof scenarios considered relevant by stakeholders are used in anautomated search for robust combinations of interventions. Theensemble of scenarios consists of climate change impactedhydrological flows, plausible water demands, environmentallymotivated abstraction reductions, and future energy prices. Theapproach is demonstrated by exploring portfolios of alternativewater infrastructure and conservation investments for London’swater supply for an estimate of conditions in 2035. We use visualanalytics to investigate the trade-offs between performance goalsand communicate the influence of specific interventions on aportfolio’s performance. Robust portfolios from a multi-scenariosearch are compared to those developed when considering onlyhistorical conditions to highlight the benefits of explicitlyconsidering multiple futures within the investment portfoliosearch. Visualizing the individual interventions implemented inthe identified portfolios from both single and multi-scenariosearch aids the exploration of how the options affect therobustness of the system. The proposed multi-scenario efficienttrade-off analysis is a valuable investment screening tool for utilityplanners identifying robust infrastructure and conservationinvestment bundles that provide benefits over a wide range offuture conditions. We believe such an approach is particularlyvaluable where decisions on resource development are contestedand trade-offs need to be negotiated with stakeholders interestedin a diverse set of definitions for desirable system performance.

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The approach is described in the Methods section. Section 3introduces the Thames basin water resource system, planningcontext, and details the optimization formulation and thescenarios of future conditions. Results are presented in Section 4and discussed in Section 5.

2. Methods

Least-cost optimal plans are typically identified using baselinehistorical conditions and tested against multiple realizations offuture conditions, particularly in the UK planning context(Environment Agency et al., 2012; Thames Water, 2013). Linkingto this standard evaluation scheme we apply a many-objectiveapproach considering a range of supply and demand managementinterventions as decisions and a combination of financial,engineering and environmental objectives (detailed in Section 3.1).A deterministic baseline is developed using only historicalhydrological conditions and demands estimated for the year2035 (i.e., a single deterministic scenario of the future) as apreliminary screening for the Thames basin water supply anddemand investments. We then implement a multi-scenario many-objective optimization approach that incorporates multipleplausible realizations of future conditions of concern to plannerswith the same problem formulation as above, with the onlydifference being that the objective values are assessed across theensemble of scenarios. Decisions are evaluated against all possiblecombinations of considered future changes in external conditions;solutions that work well across the multiple future states aresought via the multi-objective multi-scenario optimization. Theresults of the two approaches are then compared. Lastly, solutionsfrom the deterministic optimization are subjected to the multiplescenarios of the 2nd problem. Deterministic solution performanceis contrasted with that of the multi-scenario solutions to assess theadvantages of considering multiple futures whilst searching. Fig. 1illustrates the steps performed in this study.

Fig. 1. Flow chart showing the steps of the two approaches followed in the study.Two separate optimizations, deterministic (left) and multi-scenario (right), wereperformed and the results analyzed. The deterministic solutions were thensimulated against the multiple scenarios and their performance was compared tothat of the multi-scenario solutions.

2.1. Simulation-Optimization framework

This study applies a multi-objective evolutionary algorithm(MOEA) linked to a water resource system simulator where thesimulator is used to assess the performance of different portfolios.MOEAs are heuristic global search algorithms that simulate theprocess of natural evolution and are able to optimize over manyobjectives (Coello Coello et al., 2007). Rather than generating asingle optimal solution, MOEAs produce Pareto optimal sets ofsolutions, i.e., solutions which cannot be further improved in oneobjective without simultaneously reducing performance in anoth-er (Coello Coello et al., 2007; Kollat and Reed, 2006). When dealingwith complex ‘real-world’ problems the “true” Pareto optimal set isunknown; a close approximation of the Pareto optimal set istherefore generally sought (Herman et al., 2014), hence our use ofthe term ‘Pareto-approximate’ or ‘approximately Pareto optimal’.For simplicity this is referred to as Pareto optimal in the followingtext. MOEAs coupled with simulation have been shown to besuitable for complex water resource management and planningapplications (Maier et al., 2014; Nicklow et al., 2010; Reed et al.,2013), including reservoir operation (Chang et al., 2005; Chang andChang, 2009; Giuliani et al., 2014; Hurford et al., 2014), and urbanwater supply operation (Cui and Kuczera, 2003, 2005). This studyutilizes the Epsilon-dominance Non-dominated Sorting GeneticAlgorithm II (e-NSGAII) (Kollat and Reed, 2006), a description ofwhich is provided in the Supplementary material.

The MOEA is linked to an Interactive River-Aquifer Simulation2010 (IRAS-2010) (Matrosov et al., 2011) model of the Thamesbasin water resource system. The MOEA generates decisionvariables such as reservoir capacity which are passed to thesimulation model as input in addition to other input variables suchas inflows, network composition, operating rules, etc. The latterthen simulates the system quantifying flow and storage at systemnodes (reservoirs, junctions, abstractions, aquifers, treatment anddesalination plants, etc.) and links (rivers, pipes, water transfers)using a weekly time step. Performance metrics such as supplyreliability are calculated at the end of the simulation and passed toMOEA as objective values. The optimization objectives cantherefore be explicitly based on the physical performance of thesystem. IRAS-2010 Thames model has been shown to successfullyemulate a model maintained by the environmental regulatorEnvironment Agency (Matrosov et al., 2011). Surface storage in thebasin is aggregated into a single reservoir node, the LondonAggregate Storage (LAS), while the main demand in the system isrepresented by the London aggregate demand.

3. Case study

The Thames basin is located in the south-east of England and isthe driest part of Britain with an average annual precipitation ofjust 500 mm (Wilby and Harris, 2006). The population density isfour times higher than that of the rest of England, which results inmore than half of the effective rainfall being used for the publicwater supply (Merrett, 2007). Water availability in the region isthreatened by possible changes in rainfall patterns. The UK ClimateProjections (UKCP09) (Murphy et al., 2009) estimate a 15% increasein winter precipitation and an 18% decrease in summer in theLondon area under the SRES A1B medium emissions scenario whencompared to the 1961–1980 baseline conditions (EnvironmentAgency, 2009). Thames Water Utilities Ltd. (TWUL), whichmanages most of the Thames basin water resources, projects a25% increase in population in the region by 2040 (Thames Water,2014). This “expected” future is nevertheless highly uncertain. TheThames basin with existing and possible new water resourceinfrastructure is shown in Fig. 2. A description of the supply and

Fig. 2. Current and possible future supply options in the River Thames basin (adopted from Matrosov et al., 2015).

I. Huskova et al. / Global Environmental Change 41 (2016) 216–227 219

demand management interventions as well as the basin isprovided in the Supplementary material.

The non-linear seasonal Lower Thames Control Diagram (LTCD)(refer to Matrosov et al., 2011; and the Supplementary material)specifies when drought-alleviating supply schemes should beactivated based on the London Aggregate Storage (LAS) volumes.The LTCD also dictates when the minimum environmental flows inthe Thames downstream of all abstractions at Teddington shouldbe lowered and when water-use restrictions are imposed. Thethresholds vary depending on the period of the year. The Levels ofService (LoS) then specify the maximum frequency of imposing theassociated water-use restrictions on customers (Table 1), which areused as constraints in our problem formulation (Section 3.1).

Planners use the ‘Economics of Balancing Supply and Demand’(EBSD) framework (Padula et al., 2013; UKWIR, 2002) to identifythe least-cost portfolio of new water supply and conservationinterventions. EBSD is a planning method that seeks to minimizethe financial costs of meeting future water demands over a 25–30 year planning horizon given portfolios of different supply anddemand management interventions and Levels of Service.Although the current least-cost planning guidelines do considerfinancial, social and environmental costs, they require monetiza-tion and aggregation of all criteria (Environment Agency et al.,2012; Padula et al., 2013). The Water Resources Planning Guide-lines (WRPG) (Environment Agency et al., 2012) encourage watercompanies to iterate over the identified least-cost plan to find theoptimum balance between the financial, environmental and social

Table 1Constraint values based on LTCD diagram and TWUL's Levels of Service (Thames Wate

LTCD Demand Level Average annual frequency of restri

1 1 in 5 years

2 1 in 10 years

3 1 in 20 years

4 Never

costs as well as non-monetary environmental benefits. The finalplans are tested for their supply reliability and resilience. Thesetests are however performed post-optimization. Our proposedapproach explicitly takes into account these metrics within theoptimization and helps to identify plans that demonstrate all ofthese characteristics. The metrics are described in the followingsection and the Supplementary material.

3.1. Many-objective problem formulation

The London water supply problem described above wasformulated to demonstrate the benefits of incorporating manyperformance objectives within the optimization of alternativeinvestment portfolios. This section describes the objectives,decisions, and constraints used in the formulation. The perfor-mance objectives in this study consider the financial (capital,f CapCost , and energy, f Energy, cost), engineering (supply deficit, f SupDef ,reliability, f SupRel, and resilience, f SupRes) and environmental (eco-deficit, f Eco) performance of the system. Some of the objectivesused in the previous study (Matrosov et al., 2015) were changedafter a consultation with stakeholders. In particular, the operatingcost objective here includes only the cost of energy required tooperate the system to assess the effects of possible energy pricechange explicitly. The resilience objective that minimizes theduration of failures considers the maximum duration of failurehere instead of the average duration in the previous study. Theenvironmental performance is assessed by comparing the natural

r, 2014).

ctions Constraint value referring to supply reliability

C1�80%C2� 90%C3� 95%C4 = 100%

220 I. Huskova et al. / Global Environmental Change 41 (2016) 216–227

and simulated flows in the river Thames rather than using theshortage index associated with a fixed river flow volume as was thecase previously. The storage vulnerability objective maximizingthe minimum aggregate storage level in the previous study is notincluded here as the reliability and resilience objectives wereconsidered sufficient to assess the London’s aggregate storageperformance. The same proposed future supply and demandmanagement interventions are considered as decisions as inMatrosov et al. (2015). These include the Upper Thames Reservoir,River Severn Transfer, Northern Transfer, Columbus transfer, SouthLondon Artificial Recharge Scheme (SLARS), a water reuse schemeand a new desalination plant (Fig. 2). Demand managementoptions include active leakage control, a pipe repair campaign (i.e.,main pipes replacement), water efficiency improvements, instal-lation of meters, and implementation of seasonal tariffs. The UpperThames Reservoir, River Severn Transfer, and Northern Transfersupply interventions are mutually exclusive where only one ofthese interventions can be implemented within a single portfolio.

This study considers two formulations: a deterministicapproach and a multi-scenario approach. The deterministicapproach where the portfolios are evaluated against a singlefuture scenario based on historical conditions uses a single valuefor each objective. In the multi-scenario optimization portfoliosare identified as robust when they perform satisfactorily well overthe considered range of external conditions in the form ofscenarios. The performance metrics are calculated for each futurescenario in the same way as for the deterministic case. We thencalculate the average and the worst 95th percentile of valuesobtained from all scenarios to assess performance across theensemble of scenarios. The percentile values here do not have aprobabilistic interpretation but refer to the fraction of consideredcases where an outcome occurs. Water planners are typically riskaverse and will want to consider system performance understressful conditions. The worst 95th percentile performance valuereflects how a candidate solution would perform if nearly worst-case conditions occurred and is applied to metrics related tosystem failure (in our study, reliability and resilience).

The feasibility of portfolios is constrained by the mutualexclusivity of certain supply interventions and by meeting theminimum Levels of Service across the ensemble of scenarios(Table 1). In this work we assume water managers are interested insolutions that are able to satisfy today’s minimum performancelevels over a wide range of plausible future conditions. For thisreason, current Levels of Service are applied to all future scenariosas constraints. The failure frequency, i.e., the frequency of imposingdemand restrictions (Table 1), is calculated for each scenario. If acandidate solution violates any of the constraints in any scenario, itis not brought forward into the trade-off space. Keeping the currentLevels of Service limits the solutions to only those that would beacceptable under current planning goals. This does not considerthat, in response to a changing climate, future managers maydecide 2015-era Levels of Service are too strict. The problemformulation is defined by Eqs. (1)–(3):

Minimize F xð Þ ¼ f CapCost; f SupDef ; f SupRes; �f SupRel; f Eco; f Energy� �

ð1Þ

x ¼ Yi; Capif g

Yi 2 0; 1f g8i 2 V

subject to Ck� FRk (2)

Si2ME Yi � 1 ð3Þwhere x is a vector representing a portfolio of supply and demandinterventions, Yi is a binary variable representing the inclusion ofintervention i in portfolio x (1 means the intervention is includedand 0 not included), Capi is a real variable associated with thecapacity/release value of intervention i, V represents the wholedecision space, ck is a constraint associated with Level of Service(LoS) k, FRk is the value of maximum failure frequency in eachscenario allowed for LoS k, and ME represents the set of mutuallyexclusive interventions. The individual objectives and constraintsare described in more detail in the Supplementary material.

3.2. Scenarios of future conditions

One of the most widely applied approaches to incorporateuncertainties into planning is using scenarios of plausible futureconditions. The economic regulator for the UK water industryOfwat (Ofwat, 2013) requires water companies to assess key risksof their proposed plan. Planners evaluate these risks postoptimization by testing their preferred plans against plausiblefutures using scenario simulation. However, the preferred least-cost portfolio is still identified considering only baseline historicalconditions. TWUL identified and used for scenario testing fourexternal conditions with the highest potential to adversely impacttheir water resources system, based on Ofwat’s recommendations(Thames Water, 2014). These include climate change impact onhydrological flows, demand growth, sustainability reductions fromstricter environmental regulations and energy prices. The scenari-os for the four uncertainties were selected by TWUL to span therange of conditions that they would like their system to be able torespond to (Thames Water, 2014). For the purpose of our study weuse the same scenarios as identified by TWUL and consider all oftheir possible combinations for the simplicity and ease ofcommunication. The ensemble, which is incorporated within theoptimization, includes 11 hydrological flow scenarios, 2 demandlevels, 2 sustainability reductions levels and 2 energy pricescenarios resulting in the total of 88 scenarios of future conditions(Table 2).

3.2.1. Supply-side scenariosThe WRPG guidelines (Environment Agency et al., 2012) require

assessing the effects of climate change on the supply availabilityand recommend four different approaches to do so. Two of theseapproaches use 11 Future Flows (FFs) hydrological flow scenarios.The FFs scenarios represent equally probable hydrological scenari-os characterized by future climate change impacted river flowtime-series. The time-series were developed by the ‘Future Flowsand Groundwater Levels’ project (Prudhomme et al., 2013) and areavailable from the National River Flow Archive (NRFA) onlinedatabase (Centre for Ecology and Hydrology, 2012). The scenarioswere derived from the set of transient climate projections obtainedfrom the Met Office Hadley Centre Regional Climate Model(HadRM3-PPE) by dynamically downscaling the global climatemodel (Hadley Centre for Climate Predictions and Research, 2008).The model was run for the UK climate projections under thehistorical and medium emissions scenario (SRES A1B) and was alsoused to derive the UK Climate Projections scenarios produced in2009 (UKCP09) (Murphy et al., 2009). TWUL applied FFs for theirscenario testing (Thames Water, 2014). The SRES emissionscenarios (IPCC, 2000) provide emission projections assumingno mitigation policies; the IPCC has recently produced theRepresentative Concentration Pathways (RCP) scenarios that takeinto account the current legislation on air pollutants projecting

Table 2Future scenarios. All combinations of future conditions were considered in the multi-scenario robust optimization.

Uncertainty dimension Number of scenarios Future conditions

Hydrology 11 See Section 3.2.1Water demand 2 2325 ML/day

2558 ML/day

‘Sustainability reductions’ to water licenses 2 No reduction (current licensed)Total of 175 ML/day reduction

Energy unit price 2 13 p/kWh35 p/kWh

Total number of scenarios 88

I. Huskova et al. / Global Environmental Change 41 (2016) 216–227 221

lower anthropogenic emissions (Kirtman et al., 2013). Climateprojections obtained using the RCP scenarios may thereforeprovide different magnitude of change for temperature andprecipitation.

The flow time-series for the Thames basin were generated bythe hybrid hydrological model CLASSIC (Crooks and Naden, 2007),a semi-distributed grid-based rainfall–runoff model that uses acombination of regionalized and catchment calibrated parameters.The entire time series of all 11 members of the Future Flowsscenario ensemble (afgcx, afixa, afixc, afixh, afixi, afixj, afixk, afixl,afixm, afixo, and afixq) covers the period between 1950 and 2098(Prudhomme et al., 2013).

This study uses a 30-year period (2020–2050) of all 11 scenariosfor simulating demands and energy prices estimated for 2035where each of these 30 years is assumed to represent possibleconditions in the year 2035. A more detailed description, analysisand justification of the used time-series is provided in theSupplementary material.

3.2.2. Socio-economic and regulatory scenariosThe scenarios representing the socio-economic and regulatory

uncertainties for the year 2035 were chosen based on TWUL’sestimates (Thames Water, 2014) and the Ofwat’s recommenda-tions (Ofwat, 2013). The socio-economic uncertainty is repre-sented by two demand projection scenarios and two energy pricesscenarios. The two demand scenarios use the estimate of demandsfor 2035 of 2325 Ml/d and 2558 Ml/d, a 10% increase. These valuesare adjusted for each month of the year by applying monthlyfactors used by the Environment Agency’s commercial Aquatormodel. The demand of 2325 Ml/d was estimated by TWUL (ThamesWater, 2014) based on the WRPG recommendations to incorporatethe population growth estimations from local authorities andseveral assumptions such as continuation of the current meteringpolicies, maintaining leakage at the 2015 levels, etc. (EnvironmentAgency et al., 2012). The 10% increase is used by TWUL to accountfor the errors in estimates (Thames Water, 2014).

The energy price scenarios include an energy cost of 13p/kWhand 35p/kWh. The estimate of 13p/kWh uses the Department ofClimate and Energy medium forecasts for industrial energy prices.The increase to 35p/kWh was estimated by TWUL by doubling theforecasted price to account for possible carbon price increases,network replacements and upgrades, energy price increases, etc.(Thames Water, 2014).

The institutional uncertainty is represented by two sustain-ability reduction scenarios. These reflect a possible reduction in thelicensed abstraction volumes for water companies. TWUL current-ly abstracts from several locations on the River Thames and RiverLee. The IRAS-2010 Thames model aggregates the surface waterabstractions to a single abstraction node upstream of TeddingtonWeir on the River Thames and downstream of Feildes Weir on theRiver Lee, as well as a single groundwater abstraction point for thewhole basin. The reductions are therefore applied to these single

abstraction nodes. One scenario assumes no license change (i.e.,that the company will be able to abstract the current volumes in2035) while the other includes a reduction of 25 ML/d ingroundwater and 100 ML/d and 50 ML/d in surface water fromthe River Thames and River Lee, respectively, provided by theEnvironment Agency as a plausible future reduction (ThamesWater, 2014).

3.3. Computational details

The deterministic optimization was performed using a 30-yearhistorical time-series of river flows (1970–2000) with a weeklytime-step and demand and energy estimates for the year 2035. Asin Matrosov et al. (2015) this implies that we use 30 years ofhistorical hydrology to represent hydrological conditions that weassume to be representative of those that may occur in the year2035. The MOEA optimization was run for 25,000 functionevaluations (FEs) 50 times, each with a different random seedvalue to lessen the influence of random number generation on theresults. As the “true” Pareto optimal set is unknown, closeapproximation to this set was sought (Section 2.1). The referenceset (obtained by non-dominated sorting of the 50 solution setswhere any dominated solution, i.e., a solution that does notperform better against any objective when compared to the othersolutions, thus is not Pareto optimal, is discarded) was almostidentical to the Pareto optimal solutions obtained from a singleseed analysis.

The MOEA algorithm in the multi-scenario optimization wasrun for 50,000 FEs with 10 random seeds. In the multi-scenarioruns, a higher number of function evaluations were required due tothe computational complexity of solving that case. Fewer randomseeds (10) were used here than in the deterministic case (50) inorder to reduce the computational burden. The obtained referenceset again closely resembles the Pareto optimal solutions from asingle seed analysis.

4. Results

4.1. Deterministic optimization analysis

In this section we present the deterministic optimizationresults where only a single future scenario based on historicalconditions is considered. The many-dimensional visualizationoffers a rich view into high performing combinations ofinterventions and their impacts (as demonstrated in Matrosovet al. (2015)). That study showed how progressively visualizing theperformance dimensions helps communicate many-dimensionaltrade-offs and aids stakeholder understanding and deliberation. Inthis paper we assume stakeholders are familiar with multi-dimensional trade-off interpretation and show plots with alldimensions of performance (six) concurrently and focus ondisplaying graphically the benefits of incorporating uncertainty

222 I. Huskova et al. / Global Environmental Change 41 (2016) 216–227

explicitly within investment screening. The Pareto optimalsolutions here differ slightly from the solutions in our previousstudy due to different objectives used and the shorter simulationperiod in the former.

Fig. 3 shows the full set of Pareto optimal portfolios obtainedfrom the six objective optimization. The figure reveals two distinct“fronts” with one front skewed to the right, i.e., higher capital costs(shown on x axis in Fig. 3) are required to achieve identicalreliability between the right and left fronts. By improving thereliability of the system (downward direction on the vertical axis)one can also decrease supply deficits (shown on y axis in Fig. 3).Nevertheless, many perfect reliability solutions (at the bottomplane of the cube in Fig. 3) exhibit varied supply deficit thatdecreases with higher capital investment. The color scaledistinguishes the portfolios according to their environmentalperformance, i.e., the eco-deficit objective. The red pointsrepresent the highest eco-deficit, i.e., the worst environmentalperformance, while the blue points show the lowest achievableeco-deficit, i.e., the lowest environmental impact. Portfolios withthe same level of reliability differ in terms of their environmentalperformance; reducing the eco-deficit requires higher capitalinvestment. The orientation of the cones in Fig. 3 shows theresilience of the portfolios where the cones pointing upwardsindicate the worst resilience, i.e., the longest maximum duration ofLTCD Demand Level 3 failure, while the cones pointing downwardsshow the best achievable resilience. This performance objective isstrongly correlated with reliability; improving the system’s supplyreliability also increases the supply resilience, i.e., reduces theduration of the failure state.

Visualizing the energy cost objective, however, reveals poten-tially unexpected information about the system. This objective isrepresented by the size of the cones in Fig. 3 where the bigger thecone the higher the average annual operating cost the portfoliorequires. Both of the two distinct fronts (discussed further inSection 4.2.2) indicate that improving the system’s engineeringand environmental performance requires higher energy use. Moreimportantly, the portfolios on the left hand side front in Fig. 3exhibit higher energy cost requirements than the portfolios on the

Fig. 3. Pareto optimal portfolios obtained by deterministic optimization. Theprincipal axes show the capital cost, supply deficit and reliability objectives. Theeco-deficit objective is depicted by the color scale; the red solutions illustrate thehighest eco-deficit while the blue solutions show the lowest eco-deficit. Theorientation of the cones illustrates the resilience of portfolios and the size of thecones the energy cost requirements. Cones pointing upwards indicate worstresilience while cones pointing downwards the best resilience; the bigger the conethe higher energy use the portfolio requires. The arrows point towards the directionof preference, i.e., the ideal point would lie in the lower central corner of the cubeand its cone would be of the smallest size, blue color and pointing directlydownwards. Given the inherent trade-offs between the objectives, such perfor-mance cannot be achieved. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)

right hand side of the plot. Although the latter require highercapital investment to achieve similar engineering performance,these portfolios are also able to achieve lower eco-deficit (color inFig. 3) than the former. Furthermore, lower average annual energycost requirements might influence the total long-term cost of aportfolio.

4.2. Comparison of deterministic and multi-scenario optimizationresults

4.2.1. Portfolio performanceFig. 4 illustrates how the Pareto front changes when we

incorporate multiple sources of uncertainty in the form ofscenarios into the optimization. The individual objectives arerepresented as defined in Fig. 3. The translucent points show thedeterministic optimization results analyzed in the previous sectionwhile the full colored points show the multi-scenario optimizationPareto optimal portfolios. The figure indicates the uncertaintiescause the objective space to shrink and shift slightly towards theright hand side of the cube, i.e., towards higher capital investment.Achieving absolute reliability under a range of plausible futuresrequires higher capital investment than when only deterministicconditions are considered. The range of the objective values islower for the multi-scenario solutions than for the deterministicsolutions. For instance, the annualized capital cost of portfoliosvaries between £18.2m/a and £65.6m/a for the former while thelatter has values between £9.1m/a and £64.4m/a. This suggests thatthe higher variability of external conditions requires higher capitalinvestment to maintain good engineering and environmentalperformance.

The multi-scenario optimization solutions (full-colored conesin Fig. 4) achieve similar levels of reliability and resilience in variedconditions with better environmental performance at the expenseof higher capital and operating costs as compared to the

Fig. 4. Multi-scenario Pareto optimal portfolio trade-offs (full color cones)compared to the deterministic Pareto optimal portfolio trade-offs (translucentcones). The multi-scenario optimization objective space shrinks and shifts towardshigher capital and energy cost requirements (i.e., the full color cones positionedfurther from the ideal point on the capital cost axis and bigger than the translucentcones). These multi-scenario efficient portfolios attain good engineering perfor-mance despite the higher variability of stresses while outperforming thedeterministic portfolios in the ecological objective (color scale). Please note thatthe translucent deterministic solutions and the full colored multi-scenariosolutions were evaluated against different future conditions and are thereforenot directly comparable. The plot highlights how the optimal space changes andshifts when multiple sources of uncertainty are considered.(For interpretation ofthe references to colour in this figure legend, the reader is referred to the webversion of this article.)

I. Huskova et al. / Global Environmental Change 41 (2016) 216–227 223

deterministic solutions (translucent cones). It is worth noting,however, that the highest energy cost value does not significantlyexceed the highest value obtained by deterministic optimization.The similar engineering performance of the two Pareto optimalsets of portfolios can be explained by the Levels of Serviceconstraints ensuring the acceptability of the system’s behaviorunder varying future conditions. The two distinct fronts present inthe multi-scenario results differ in terms of the operating costrequirements as was the case in the deterministic solution set(Fig. 3).

4.2.2. Portfolio compositionFig. 5 compares portfolio composition (i.e., how interventions

map to the performance objective space) between the determin-istic (left) and multi-scenario (right) results in the same view asshown in Figs. 3 and 4. The size of the cones illustrates the energycost requirements of portfolios. The color represents the imple-mentation of the mutually exclusive supply options; green conesshow portfolios that include the Upper Thames Reservoir (UTR),the red colored portfolios incorporate the unsupported RiverSevern Transfer (RST), and blue cones depict portfolios that do notimplement any of these. The deterministic Pareto optimalportfolios implement a combination of these. When none of thesenew supply interventions are implemented portfolios require thelowest capital investment but have the worst supply reliability.Most of the Pareto optimal portfolios implement the UTR and onlya fraction implement the RST. The latter (red points in Fig. 5)exhibit perfect reliability but these portfolios require the highestoperating energy use, possibly making them impractical in thelong-term. None of the multi-scenario Pareto optimal portfolios(right panel in Fig. 5) implement the transfer intervention whichrequires higher capital and operating costs than the reservoir; allbuild the UTR reservoir.

The orientation of cones in Fig. 5 indicates implementation ofthe Pipe repair demand management intervention for the LondonWater Resource Zone (WRZ); cones pointing upwards depictportfolios that include the Pipe repair campaign while conespointing downwards show portfolios that do not. Both panels showa combination of portfolios with and without the Pipe repaircampaign creating the two distinct fronts. Portfolios implementing

Fig. 5. Comparison of portfolio composition between the deterministic and multi-scenarand 4. Cone size represents the portfolio energy cost while color shows which of the muwhether or not each portfolio implemented the London pipe repair campaign. Implemencones pointing downwards) the pipe repairs divides the trade-off space into two distinct

is referred to the web version of this article.)

this intervention require higher capital investment but exhibitbetter environmental performance (color of cones in Fig. 4) anddemand lower energy use (size of cones in Fig. 5) than theportfolios on the left front. This suggests the demand managementinterventions may help improve the system’s performance withreduced energy consumption. All of the multi-scenario Paretooptimal solutions implement all the other demand managementinterventions for the London WRZ (i.e., active leakage control,efficiency improvement, metering, and seasonal tariffs). Demandmanagement interventions may therefore be considered toincrease the robustness of plans against uncertain futureconditions.

4.3. How deterministic solutions would perform under uncertainty

Intervention portfolios developed whilst considering onlyhistorical conditions (i.e., deterministic optimization) might notperform well under conditions that are possible in an uncertainfuture. To demonstrate the potential bias in this approach we selectsix representative solutions (supply and demand managementportfolios) from the deterministic Pareto optimal front. The sixportfolios are highlighted in Fig. 6 by full color points while thetranslucent points depict the whole set of Pareto optimal solutionsfrom the deterministic (left) and multi-scenario (right) optimiza-tion. The portfolios are distinguished by indicative namesreflecting their capital investment requirements or implementa-tion of one of the mutually exclusive supply interventions. TheLeast Cost portfolio does not implement any of the mutuallyexclusive strategic supply interventions and requires the lowestcapital investment. The Reservoir 1 and 2 portfolios build the UTR,exhibit the same performance against the reliability objective butdiffer in the capital investment requirements. The more expensiveReservoir 2 portfolio implements the Pipe repair campaigndemand management intervention for the London WRZ, whilethe cheaper Reservoir 1 portfolio does not. The Reservoir 3portfolio also implements the UTR and Pipe repair campaign butrequires even higher capital investment which results in perfectreliability. The Transfer portfolio implements the RST and achieves100% reliability. The Highest Cost portfolio achieves perfectreliability by implementing all considered supply (including

io Pareto optimal solutions. The cardinal axes show the same objectives as in Figs. 3tually exclusive supply interventions was implemented. Cone orientation indicatesting (lighter colored cones pointing upwards) or not implementing (darker coloredfronts.(For interpretation of the references to colour in this figure legend, the reader

Fig. 6. Six representative deterministic (left) Pareto optimal portfolios (large fullcolor spheres in the left panel) were simulated under the 88 future scenarios. Theperformance of these solutions over the future scenarios is compared to that of themulti-scenario Pareto-approximate optimal solutions (full color spheres vstranslucent cones, respectively, in the right panel). Only two portfolios (Reservoir3, Highest Cost) satisfy the LoS constraints when subjected to the multiple scenariosbut are dominated by other portfolios (they show higher capital costs thanportfolios with the same reliability). Please note that while these two solutionswere Pareto optimal under deterministic conditions, they are not Pareto optimalunder the 88 possible scenarios. The two-dimensional plots are projections of a six-objective frontier onto a two-dimensional surface and as such show only the trade-off between the two plotted dimensions.(For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

224 I. Huskova et al. / Global Environmental Change 41 (2016) 216–227

UTR) and the majority of demand interventions and requires thehighest capital investment.

The six solutions were simulated under the same 88 scenariosthat were used in the multi-scenario optimization. Whensubjected to the multi-scenario conditions only two of the sixportfolios satisfy the LoS constraints as calculated over thescenario ensemble. The performance of these two portfolios(Reservoir 3 and Highest Cost) under multiple future conditions isshown in the right panel in Fig. 6 (full color points) and comparedto the multi-scenario Pareto optimal portfolios (translucent conesin the right panel of Fig. 6). These two solutions exhibit worsereliability performance under the 88 future scenarios than they didunder the deterministic analysis. In fact, both of these portfoliosexhibit worse performance in all other objectives under uncer-tainty (summarized in Table 3). The operating costs show thehighest difference indicating that to satisfy the Levels of Serviceunder higher variability of conditions the system would need tooperate more intensively resulting in higher operating expendi-ture.

To illustrate the importance of incorporating uncertaintydirectly into the optimization the whole deterministic Paretooptimal set of solutions was simulated over the 88 scenarios. Only40% of this set satisfied LoS constraints when calculated over all 88plausible future scenarios. These surviving solutions were thensorted amongst each other to preserve only the dominatingsolutions in the set, discarding majority of these solutions. Only 3%

Table 3Performance comparison of the Reservoir 3 and Highest Cost portfolios depicted in Fig

Objective Reservoir 3

Deterministic Mul

Supply deficit (%) 1.20 2.63Supply resilience (weeks) 0 8

Supply reliability (%) 100 99.5Eco-deficit (%) 56 57

Energy cost (£m/a) 5.56 7.87

of the original deterministic Pareto optimal solutions were left.While these solutions were Pareto optimal under deterministicconditions, they are not Pareto optimal under the 88 possiblescenarios.

Fig. 7 illustrates how the performance of these remainingsolutions compares to that of the multi-scenario Pareto optimalsolutions. The latter are shown as opaque while the former aredepicted by translucent points. The two panels show two differentviews of the same solution sets. When subjected to the 88 futurescenarios, the remaining deterministic solutions (translucentspheres in Fig. 7) are dominated by the multi-scenario Paretooptimal solutions (full color spheres in Fig. 7), i.e., they can nolonger be considered Pareto optimal. The translucent portfoliosrequire higher capital investment and energy use (shown by thesize of points in Fig. 7) to achieve the same levels of reliability thanthe full colored portfolios (that are located in the same positionregarding the vertical axis of Fig. 7a). The latter also require lowercapital investment and energy use to maintain the same levels ofsupply deficit than the former, also exhibiting better environmen-tal performance (shown by color in Fig. 7). This is particularlyvisible in Fig. 7b where the same set of portfolios as in Fig. 7a isshown in different view; the reliability and supply deficit axeswere switched and the plot rotated anticlockwise. The full coloredspheres require lower capital and operating cost as they are closerto the ideal point with respect to the capital cost axis and of lowersize than the translucent spheres.

5. Discussion

5.1. Many-objective optimization

Water resource systems serve stakeholders with complex andvarying interests who may have differing preferences regardinghow the system should be able to adapt in the context of futureuncertainty (Heffernan, 2012). It is therefore desirable to integratethese multiple needs in the decision making process (Simpson,2014) and provide decision-makers with the ability to consider thebroader consequences of various decisions (Loucks, 2012). Multi-objective optimization allows planners to incorporate differentand often conflicting preferences into decision making. Optimizingfor these preferences explicitly, without the need to monetize andaggregate them into a single objective, allows decision makers tovisually assess the trade-offs that different investments imply.Trade-offs can facilitate stakeholder deliberations post optimiza-tion and provide planners with a rich view into high performingintervention portfolios that otherwise would remain hidden iflower dimensional analysis (monetary only) was used. In theThames basin, reducing capital investments negatively affects theengineering and environmental performance of the system (Fig. 3).Higher capital investment results in maintaining good engineeringand environmental performance whilst saving on energy costs.Decision makers who value reliability and good environmentalperformance without a large increase in energy use may choose aplan from the portfolios in the lower part of the right front in Fig. 3.

. 6 between the deterministic and multi-scenario conditions.

Highest Cost

ti-scenario Deterministic Multi-scenario

0.35 1.350 2

0 100 99.8751 54

9.30 13.69

Fig. 7. Deterministic Pareto optimal solutions that comply with the LoS constraints under the multi-scenario conditions (translucent points) and the multi-scenario Paretooptimal solutions (full colored points) visualized together. The cardinal axes show the same objectives as Figs. 3, 4 and 5. Color represents the environmental performance ofportfolios while the size of the points indicates their energy costs. The deterministic solutions are dominated by the multi-scenario efficient solutions (i.e., their positions,colors, and sizes are further away from the ideal point than the multi-scenario solutions). Whilst deterministic solutions were Pareto optimal under historical conditions, theyare not Pareto optimal under the 88 plausible scenarios.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of thisarticle.)

I. Huskova et al. / Global Environmental Change 41 (2016) 216–227 225

5.2. Incorporating uncertainties into many-objective optimization

When planning under uncertainty planners should ensure theirsystem is able to cope with a wide range of plausible futures. Ourstudy illustrates that taking into account multiple performanceobjectives and planning for robustness can be achieved concur-rently. Deterministic optimization of the Thames water resourcesystem interventions considering only the historical flow recordwas compared to a multi-scenario optimization which consideredmultiple sources of uncertainty. We found that using historicalflow records to assess future system investments can providebiased information about individual portfolios, i.e., make themseem favorable when in fact they do not perform well in manyalternate plausible futures. Fig. 6 illustrated how the performanceof six representative solutions from the deterministic optimizationanalysis changes subject to multiple sources of uncertainty. Onlytwo solutions remain feasible (Reservoir 3 and Highest Cost inFig. 6) but show worse performance against the optimizedobjectives than suggested by the deterministic approach (Table 3).In total 60% of portfolios considered Pareto optimal in thedeterministic analysis fail under the wider set of future conditionswith only 3% of the original set surviving non-dominated sorting(see the first paragraph of Section 3.3). Fig. 7 showed that themulti-scenario portfolios perform better with respect to theenvironmental and economic objectives than the surviveddeterministic portfolios. By incorporating uncertainty directlyinto the optimization process one identifies robust solutions thatperform well under a range of plausible future states.

5.3. Visual analytics

Visualizing the Pareto optimal set of solutions in the many-dimensional objective space allows decision makers to discoverhow the different system performance objectives conflict andinteract with each other. Many objectives may be represented byother visualization techniques such as parallel plots (Rosenberg,2015). The many-dimensional trade-off scatter plots presentedhere highlight the interactions and conflicts between theobjectives for the purpose of this study. In our experiencecommunicating the information provided by many-objectivetrade-off plots to decision makers is best done by visualizing

dimensions progressively. The many-dimensional plot of Fig. 3only represents the final stage of the exploration. The progressiveintroduction of dimensions within trade-off plots is explored byMatrosov et al. (2015). Visualizing and exploring the Paretooptimal portfolios progressively may aid the learning and decisionmaking process and help justify to interested parties why a certainintervention was selected. Decision makers are given theopportunity to decide the balance between performance prefer-ences a posteriori. Visual analytics can provide the means tocompare the deterministic and multi-scenario optimizationobjective spaces as well as how and why their Pareto optimalportfolios differ.

Robust interventions can be identified by their presence in thePareto optimal solutions obtained from the multi-scenariooptimization. Fig. 5 showed that although some deterministicPareto optimal portfolios implement the unsupported River SevernTransfer instead of the Upper Thames Reservoir, none of the multi-scenario portfolios select the more expensive and less reliabletransfer. In contrast, the UTR is implemented in all of the multi-scenario portfolios. This suggests that, given how the system iscurrently modeled, the reservoir intervention improves the systemdesign’s robustness against a variety of future conditions. Similarly,the Pipe repair demand management intervention improves thesystem’s performance under the considered range of futureconditions. Further analysis showed that all the other demandmanagement interventions are implemented in all the robustportfolios in the London WRZ. Water companies generally preferimplementing supply-side measures to plan for future deficits(Charlton and Arnell, 2011) but our results suggest that reducingdemand by implementing demand management interventionsincreases plan robustness. These interventions do not requireenergy unlike the majority of supply interventions, do not rely onuncertain hydrological flows and are likely appropriate strategiesfor relatively water scarce systems in the face of uncertainty.

5.4. Limitations and future work

Future conditions in this study were represented in a limitedway. The set of 11 Future Flow scenarios is recommended for theclimate change impact assessment in the UK by regulators andused in the Thames basin water resource system planning

226 I. Huskova et al. / Global Environmental Change 41 (2016) 216–227

(Environment Agency et al., 2012; Thames Water, 2014). The 30-year flow time-series used here (2020–2050) may be consideredquasi-stationary at best; just over half of the scenarios do notexhibit transient characteristics during this time period (seeSupplementary material). Transient time-series, where the prob-ability distribution that characterizes the flow at any given timeperiod changes progressively as time moves forward, are notappropriate for studies considering a static snapshot of a system’sperformance in time. The sample of water demand, energy pricesand sustainability reductions was suitable in the particularplanning context (chosen in consultation with stakeholders) butit does not represent a wide range of possibilities; only 2 differentstates for each were represented. We acknowledge the short-comings of using a limited number of scenarios as well as estimatesbased on the extrapolations of current socio-economic trends toconsider uncertainty of future conditions. The purpose of the studyis to highlight the possible improvements to the current planningapproach in England, one of which is using the scenarios to identifythe robust portfolios instead of evaluating the deterministic least-cost portfolio against each of those separately. In future, a largermore diverse scenario set could be sampled and more advancedsampling techniques could be used.

Identifying robust combinations of assets is valuable but it doesnot fully serve the planning processes where investments must bechosen and prioritized over time. The approach as applied here didnot recommend a schedule of implementation (as does the currentEBSD approach); this is left to future work which will need toconsider, and trade-off, the value of flexibility (Woodward et al.,2014) and adaptation (Haasnoot et al., 2013; Hamarat et al., 2014).

The proposed approach is computationally intensive, evenwhen only 88 scenarios are considered. Our multi-scenariooptimization ran in 46 h on 96 CPU cores. Further increasing thenumber of possible future scenarios increases the number of theircombinations exponentially. Evaluating each candidate portfolioagainst such a large ensemble poses significant computationalchallenges. The ability of the MOEA optimization algorithm toconverge to the true Pareto optimal front becomes increasinglydifficult to demonstrate. Here we performed a random seedanalysis for the multi-scenario optimization with 10 differentrandom seeds (see Kollat and Reed (2006) for more details) whilethe deterministic optimization random seed analysis checked theapproximation to the true Pareto optimal set using 50 randomseeds. As more scenarios are used, it might be increasingly harderto verify the approximation sufficiently.

6. Conclusions

This paper proposed an approach to identify and visuallydisplay robust plans for water resource systems that meet manyfinancial, engineering and ecological goals. The approach wasapplied to identifying portfolios of new water supplies anddemand management interventions that could meet London’sestimated water supply demands in 2035. Proposed portfolioswere evaluated against the following metrics: annualized capitalcost, maximum annual supply deficit, supply resilience, supplyreliability, hydro-ecological deficits and annual average energycost. Future portfolios were also assessed against multiplescenarios of future climate change impacted hydrological flows,water demands, environmentally motivated abstraction reduc-tions, and energy prices. To identify the most robust portfoliosamongst the many available options we used a search algorithm(many-objective evolutionary algorithm) linked to a waterresource system simulator.

Results were presented via many-dimensional visualizationsthat help decision-makers consider how the performance objec-tives trade-off with each other for the portfolios identified as

Pareto optimal. Plots can also show how options are distributedwithin the Pareto front and how they influence the system’sperformance. The study was designed to show the benefits ofconsidering multiple plausible futures to optimize a complexsystem, rather than a single deterministic scenario. Only 3% ofdeterministic Pareto optimal solutions perform satisfactorily wellunder the set of plausible future conditions chosen by stakeholdersin our study. Multi-scenario optimization identified portfolios thatdominate those suggested by deterministic optimization. Explor-ing the Pareto optimal portfolios of supply and demandinterventions helps identifying robust interventions that providebenefits over a wide range of futures including those withconditions similar to today.

Acknowledgements

This work was funded by the UK Engineering and PhysicalScience Research Council (EPSRC grant EP/G060460/1) and ThamesWater Utility Ltd. We would like to thank Patrick Reed whoprovided suggestions and guidance in this work, and to ChrisCounsell from HR Wallingford for providing the Future Flow time-series for the River Severn at Deerhurst not available from the NRFAdatabase. Mark New, Fai Fung and Glenn Watts of the EnvironmentAgency provided advice which improved the study and presenta-tion. Only the authors bear responsibility for errors. The authorsacknowledge the use of the UCL Legion High PerformanceComputing Facility (Legion@UCL) and the Computational SharedFacility of the University of Manchester, and associated supportservices, in the completion of this work.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.gloenvcha.2016.10.007.

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